# Numerical solution of 2D-vector tomography problem using the method of approximate inverse

## Abstract

We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.

- Authors:

- Sobolev Institute of Mathematics of SB RAS, 630090, Novosibirsk (Russian Federation)
- (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22608264

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 1759; Journal Issue: 1; Conference: ICAAM 2016: International conference on analysis and applied mathematics, Almaty (Kazakhstan), 7-10 Sep 2016; Other Information: (c) 2016 Author(s); Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; APPROXIMATIONS; COMPUTERIZED SIMULATION; NUMERICAL SOLUTION; TOMOGRAPHY; TWO-DIMENSIONAL CALCULATIONS; VECTOR FIELDS

### Citation Formats

```
Svetov, Ivan, Maltseva, Svetlana, Polyakova, Anna, and Novosibirsk State University, 630090, Novosibirsk.
```*Numerical solution of 2D-vector tomography problem using the method of approximate inverse*. United States: N. p., 2016.
Web. doi:10.1063/1.4959746.

```
Svetov, Ivan, Maltseva, Svetlana, Polyakova, Anna, & Novosibirsk State University, 630090, Novosibirsk.
```*Numerical solution of 2D-vector tomography problem using the method of approximate inverse*. United States. doi:10.1063/1.4959746.

```
Svetov, Ivan, Maltseva, Svetlana, Polyakova, Anna, and Novosibirsk State University, 630090, Novosibirsk. Wed .
"Numerical solution of 2D-vector tomography problem using the method of approximate inverse". United States. doi:10.1063/1.4959746.
```

```
@article{osti_22608264,
```

title = {Numerical solution of 2D-vector tomography problem using the method of approximate inverse},

author = {Svetov, Ivan and Maltseva, Svetlana and Polyakova, Anna and Novosibirsk State University, 630090, Novosibirsk},

abstractNote = {We propose a numerical solution of reconstruction problem of a two-dimensional vector field in a unit disk from the known values of the longitudinal and transverse ray transforms. The algorithm is based on the method of approximate inverse. Numerical simulations confirm that the proposed method yields good results of reconstruction of vector fields.},

doi = {10.1063/1.4959746},

journal = {AIP Conference Proceedings},

number = 1,

volume = 1759,

place = {United States},

year = {Wed Aug 10 00:00:00 EDT 2016},

month = {Wed Aug 10 00:00:00 EDT 2016}

}

DOI: 10.1063/1.4959746

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